The missive came hours after Trump told CNN's Wolf Blitzer that he would consider skipping this Thursday's Republican primary debate if he doesn't get fair treatment from Kelly, who he said treats him "very unfairly."

"Sooner or later Donald Trump, even if he's president, is going to have to learn that he doesn't get to pick the journalists -- we're very surprised he's willing to show that much fear about being questioned by Megyn Kelly," the network said in a statement.

Trump has been accusing Kelly of unfair treatment ever since he stepped off stage at the first Fox News debate in August.

But he's ratcheted up those attacks in recent days in an apparent attempt to influence the Fox News moderators ahead of Thursday's debate.

"I don't like her. She doesn't treat me fairly. I'm not a big fan of hers at all," Trump said during Monday's interview. He also claimed that he "might be the best thing that ever happened to her," because no one had ever heard of her before the August debate.

Trump also suggested he might skip the debate unless he was confident Kelly would treat him fairly, but then walked back those remarks: "That doesn't mean I don't do the debate. I like doing the debates. I've won every single debate according to every poll."

And last week, Trump tweeted that Kelly "should not be allowed" to moderate the debate because of her "conflict of interest and bias."

Donald Trump and Fox News anchor Megyn Kelly

Fox News responded to that tweet unequivocally: "Megyn Kelly has no conflict of interest," the network said. "Donald Trump is just trying to build up the audience for Thursday's debate, for which we thank him," Fox said.